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Block #2,199,584

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/9/2017, 6:56:46 AM Β· Difficulty 10.9526 Β· 4,631,417 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
734215f3e9672259c359829e84636fd107460ec82d2a0e0d933835f73a773f84
View on Chainz β†—

Height

#2,199,584

Difficulty

10.952619

Transactions

1

Size

208 B

Version

2

Bits

0af3dedf

Nonce

121,614,232

Timestamp

7/9/2017, 6:56:46 AM

Confirmations

4,631,417

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

46b3aa8bb56f2041f611d836d694425c4b3e4626a474c8101cbcc25277dcd233
Transactions (1)
Coinbase46b3aa8bb56f20…bcc25277dcd233
1 in β†’ 1 out8.3200 XPM118 B
AM6GYpjw…aw86QDtR
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.583 Γ— 10⁹⁡(96-digit number)
35832504676460230848…35397751535152962239
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
3.583 Γ— 10⁹⁡(96-digit number)
35832504676460230848…35397751535152962239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.166 Γ— 10⁹⁡(96-digit number)
71665009352920461696…70795503070305924479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.433 Γ— 10⁹⁢(97-digit number)
14333001870584092339…41591006140611848959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.866 Γ— 10⁹⁢(97-digit number)
28666003741168184678…83182012281223697919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.733 Γ— 10⁹⁢(97-digit number)
57332007482336369357…66364024562447395839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.146 Γ— 10⁹⁷(98-digit number)
11466401496467273871…32728049124894791679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.293 Γ— 10⁹⁷(98-digit number)
22932802992934547743…65456098249789583359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.586 Γ— 10⁹⁷(98-digit number)
45865605985869095486…30912196499579166719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.173 Γ— 10⁹⁷(98-digit number)
91731211971738190972…61824392999158333439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.834 Γ— 10⁹⁸(99-digit number)
18346242394347638194…23648785998316666879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,892,149 XPMΒ·at block #6,831,000 Β· updates every 60s
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